Problem: $\dfrac{ -8m - n }{ -9 } = \dfrac{ 4m + 2p }{ 4 }$ Solve for $m$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -8m - n }{ -{9} } = \dfrac{ 4m + 2p }{ 4 }$ $-{9} \cdot \dfrac{ -8m - n }{ -{9} } = -{9} \cdot \dfrac{ 4m + 2p }{ 4 }$ $-8m - n = -{9} \cdot \dfrac { 4m + 2p }{ 4 }$ Multiply both sides by the right denominator. $-8m - n = -9 \cdot \dfrac{ 4m + 2p }{ {4} }$ ${4} \cdot \left( -8m - n \right) = {4} \cdot -9 \cdot \dfrac{ 4m + 2p }{ {4} }$ ${4} \cdot \left( -8m - n \right) = -9 \cdot \left( 4m + 2p \right)$ Distribute both sides ${4} \cdot \left( -8m - n \right) = -{9} \cdot \left( 4m + 2p \right)$ $-{32}m - {4}n = -{36}m - {18}p$ Combine $m$ terms on the left. $-{32m} - 4n = -{36m} - 18p$ ${4m} - 4n = -18p$ Move the $n$ term to the right. $4m - {4n} = -18p$ $4m = -18p + {4n}$ Isolate $m$ by dividing both sides by its coefficient. ${4}m = -18p + 4n$ $m = \dfrac{ -18p + 4n }{ {4} }$ All of these terms are divisible by $2$ $m = \dfrac{ -{9}p + {2}n }{ {2} }$